peterahunter has got it right. Find/hire a solid leader for the department who can establish trust and communications at the individual employee level - someone who "manages by walking around", is visible to the employees, listens to their problems, solicits their input on how to make things better and understands that nothing gets done without the help of the people being managed.
I made the transition to federal HR a couple of years ago from over 30 years in the private sector. It is very, very different.
Bob Lavigna's excellent response focused a lot on staffing, but the same considerations apply to all aspects of HR in the government sector, at least in the federal part. Private sector has a great deal of latitude in developing new approachs or creative solutions to existing problems provided that they're not illegal. In the government, much of what you do in response to problems or the processes you follow are statutory. The amount of annual raises are set by Congress, the process followed to investigate an EEO complaint are detailed and are not to be deviated from, discharge of employees can only be done under certain circumstances and if certain processes/criteria are met. After six months in the government, I was rather convinced that HR in the public sector was an endless series of "gotcha's" if you weren't knowledgeable and very, very careful.
Beth Sussman gave you a great response and covered the bases quite nicely.
My recommendation would be to find a generalist with a strong background in recruiting. The competition for aerospace engineering talent can be very rigorous - Beth was quite correct in placing this first on her list of what to look for. If you can't get the right people hired, the rest becomes pointless.
I think you could find a number of very experienced HR people available who would be quite willing to do this for a few years to help get you started, persons who perhaps have been HR directors in high tech/engineering and are looking for a challenge on a smaller scale with the idea that they'd develop a solid HR function and then turn it over to a successor who'll be around for a longer period. [This is the polite way of suggesting that you find someone planning to retire in 2 - 3 years].
Forget about PEO's. They're OK with administration, but this is a development project for a solid and well experienced HR professional.